Given a video \(X\)  that is composed of multiple frames \(x_1, x_2 ... x_N\)  where \(N\)  denotes the length of such video clip, the video compression process can be formulated/deemed as a rate-distortion (R-D) optimization (RDO) problem [1]}, [2]}. The target of such RDO can be understood from two sides, one is minimizing bit-rate cost, i.e.transmission/storage cost, while not increasing fidelity distortion, the other is minimizing distortion with a fixed bit-rate. The Lagrangian
formulation of the minimization RDO problem is given by:
\({\rm min}J, \hspace{5.69054pt} where \hspace{2.84526pt} J = R + \lambda D,\) 
